A Gibbons–Penrose Inequality for Surfaces in Schwarzschild Spacetime

2013/03/31 by Simon Brendle, Mu-Tao Wang, Mu‐Tao Wang · 1 citation
Mathematics · Physics and Astronomy · #Advanced Differential Geometry Research #Classical mechanics #General relativity #Geometric Analysis and Curvature Flows #Inequality #Mathematical analysis #Mathematical physics #Mathematics #Physics #Quantum mechanics #Relativity and Gravitational Theory #Schwarzschild metric #Schwarzschild radius #Spacetime #gr-qc #math-ph #math.DG #math.MP

paper · pdf · doi:10.1007/s00220-014-1972-6

11 pages. Final version. To appear in Communications in Mathematical Physics

arxiv created 2013/08/22 · openalex publication_date 2014/03/08 · arxiv updated 2015/06/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

Abstract

We propose a geometric inequality for two-dimensional spacelike surfaces in the Schwarzschild spacetime. This inequality implies the Penrose inequality for collapsing dust shells in general relativity, as proposed by Penrose and Gibbons. We prove that the inequality holds in several important cases.

Citations

• Quasilocal Mass in General Relativity
• Present status of the Penrose inequality
• Isometric Embeddings into the Minkowski Space and New Quasi-Local Mass
• A Minkowski inequality for hypersurfaces in the Anti-deSitter-Schwarzschild manifold
• Quasilocal mass and surface Hamiltonian in spacetime

Cited by

• New Heintze-Karcher type inequalities in sub-static warped product manifolds